The Model

The model is of the form:

y = b0 + (b1 * x)
p(x) = Pr(response|x) = 1 / (1 + exp(-y))

The model parameters b0 and b1 are found that minimize the negative log-likelihood of the data. This is done using numerical optimization. The Nelder-Mead simplex algorithm is used here. The code makes use of Michael Hutt's implementation of the Nelder-Mead algorithm.